# ---
# title: 1387. Sort Integers by The Power Value
# id: problem1387
# author: Tian Jun
# date: 2020-10-31
# difficulty: Medium
# categories: Sort, Graph
# link: <https://leetcode.com/problems/sort-integers-by-the-power-value/description/>
# hidden: true
# ---
# 
# The power of an integer `x` is defined as the number of steps needed to
# transform `x` into `1` using the following steps:
# 
#   * if `x` is even then `x = x / 2`
#   * if `x` is odd then `x = 3 * x + 1`
# 
# For example, the power of x = 3 is 7 because 3 needs 7 steps to become 1 (3
# --> 10 --> 5 --> 16 --> 8 --> 4 --> 2 --> 1).
# 
# Given three integers `lo`, `hi` and `k`. The task is to sort all integers in
# the interval `[lo, hi]` by the power value in **ascending order** , if two or
# more integers have **the same** power value sort them by **ascending order**.
# 
# Return the `k-th` integer in the range `[lo, hi]` sorted by the power value.
# 
# Notice that for any integer `x` `(lo <= x <= hi)` it is **guaranteed** that
# `x` will transform into `1` using these steps and that the power of `x` is
# will **fit** in 32 bit signed integer.
# 
# 
# 
# **Example 1:**
# 
#     
#     
#     Input: lo = 12, hi = 15, k = 2
#     Output: 13
#     Explanation: The power of 12 is 9 (12 --> 6 --> 3 --> 10 --> 5 --> 16 --> 8 --> 4 --> 2 --> 1)
#     The power of 13 is 9
#     The power of 14 is 17
#     The power of 15 is 17
#     The interval sorted by the power value [12,13,14,15]. For k = 2 answer is the second element which is 13.
#     Notice that 12 and 13 have the same power value and we sorted them in ascending order. Same for 14 and 15.
#     
# 
# **Example 2:**
# 
#     
#     
#     Input: lo = 1, hi = 1, k = 1
#     Output: 1
#     
# 
# **Example 3:**
# 
#     
#     
#     Input: lo = 7, hi = 11, k = 4
#     Output: 7
#     Explanation: The power array corresponding to the interval [7, 8, 9, 10, 11] is [16, 3, 19, 6, 14].
#     The interval sorted by power is [8, 10, 11, 7, 9].
#     The fourth number in the sorted array is 7.
#     
# 
# **Example 4:**
# 
#     
#     
#     Input: lo = 10, hi = 20, k = 5
#     Output: 13
#     
# 
# **Example 5:**
# 
#     
#     
#     Input: lo = 1, hi = 1000, k = 777
#     Output: 570
#     
# 
# 
# 
# **Constraints:**
# 
#   * `1 <= lo <= hi <= 1000`
#   * `1 <= k <= hi - lo + 1`
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
